Connectivity Properties Of Group Actions On Non Positively Curved Spaces
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Connectivity Properties Of Group Actions On Non Positively Curved Spaces
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Author : Robert Bieri
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Connectivity Properties Of Group Actions On Non Positively Curved Spaces written by Robert Bieri and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Generalizing the Bieri-Neumann-Strebel-Renz Invariants, this Memoir presents the foundations of a theory of (not necessarily discrete) actions $\rho$ of a (suitable) group $G$ by isometries on a proper CAT(0) space $M$. The passage from groups $G$ to group actions $\rho$ implies the introduction of 'Sigma invariants' $\Sigmak(\rho)$ to replace the previous $\Sigmak(G)$ introduced by those authors. Their theory is now seen as a special case of what is studied here so that readers seeking a detailed treatment of their theory will find it included here as a special case. We define and study 'controlled $k$-connectedness $(CCk)$' of $\rho$, both over $M$ and over end points $e$ in the 'boundary at infinity' $\partial M$; $\Sigmak(\rho)$ is by definition the set of all $e$ over which the action is $(k-1)$-connected. A central theorem, the Boundary Criterion, says that $\Sigmak(\rho) = \partial M$ if and only if $\rho$ is $CC{k-1}$ over $M$.An Openness Theorem says that $CCk$ over $M$ is an open condition on the space of isometric actions $\rho$ of $G$ on $M$. Another Openness Theorem says that $\Sigmak(\rho)$ is an open subset of $\partial M$ with respect to the Tits metric topology. When $\rho(G)$ is a discrete group of isometries the property $CC{k-1}$ is equivalent to ker$(\rho)$ having the topological finiteness property type '$F_k$'. More generally, if the orbits of the action are discrete, $CC{k-1}$ is equivalent to the point-stabilizers having type $F_k$. In particular, for $k=2$ we are characterizing finite presentability of kernels and stabilizers. Examples discussed include: locally rigid actions, translation actions on vector spaces (especially those by metabelian groups
Connectivity Properties Of Group Actions On Non Positively Curved Spaces
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Author : Robert Bieri
language : en
Publisher:
Release Date : 2014-09-11
Connectivity Properties Of Group Actions On Non Positively Curved Spaces written by Robert Bieri and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Connections categories.
Generalizing the Bieri-Neumann-Strebel-Renz Invariants, this memoir presents the foundations of a theory of (not necessarily discrete) actions $\rho$ of a (suitable) group $G$ by isometries on a proper CAT(0) space $M$. It introduces the passage from groups $G$ to group actions $\rho$ that implies the introduction of 'Sigma invariants'.
Classification And Probabilistic Representation Of The Positive Solutions Of A Semilinear Elliptic Equation
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Author : Benoît Mselati
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Classification And Probabilistic Representation Of The Positive Solutions Of A Semilinear Elliptic Equation written by Benoît Mselati and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$, this title intends to prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], answering a major open question of [Dy02].
Kahler Spaces Nilpotent Orbits And Singular Reduction
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Author : Johannes Huebschmann
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Kahler Spaces Nilpotent Orbits And Singular Reduction written by Johannes Huebschmann and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
For a stratified symplectic space, a suitable concept of stratified Kahler polarization encapsulates Kahler polarizations on the strata and the behaviour of the polarizations across the strata and leads to the notion of stratified Kahler space which establishes an intimate relationship between nilpotent orbits, singular reduction, invariant theory, reductive dual pairs, Jordan triple systems, symmetric domains, and pre-homogeneous spaces: The closure of a holomorphic nilpotent orbit or, equivalently, the closure of the stratum of the associated pre-homogeneous space of parabolic type carries a (positive) normal Kahler structure. In the world of singular Poisson geometry, the closures of principal holomorphic nilpotent orbits, positive definite hermitian JTS's, and certain pre-homogeneous spaces appear as different incarnations of the same structure. The closure of the principal holomorphic nilpotent orbit arises from a semisimple holomorphic orbit by contraction. Symplectic reduction carries a positive Kahler manifold to a positive normal Kahler space in such a way that the sheaf of germs of polarized functions coincides with the ordinary sheaf of germs of holomorphic functions. Symplectic reduction establishes a close relationship between singular reduced spaces and nilpotent orbits of the dual groups. Projectivization of holomorphic nilpotent orbits yields exotic (positive) stratified Kahler structures on complex projective spaces and on certain complex projective varieties including complex projective quadrics. The space of (in general twisted) representations of the fundamental group of a closed surface in a compact Lie group or, equivalently, a moduli space of central Yang-Mills connections on a principal bundle over a surface, inherits a (positive) normal (stratified) Kahler structure. Physical examples are provided by certain reduced spaces arising from angular momentum zero.
Moduli Spaces Of Polynomials In Two Variables
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Author : Javier Fernández de Bobadilla
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Moduli Spaces Of Polynomials In Two Variables written by Javier Fernández de Bobadilla and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Investigates the geometry of the orbit space. This book associates a graph with each polynomial in two variables that encodes part of its geometric properties at infinity. It also defines a partition of $\mathbb{C} x, y]$ imposing that the polynomials in the same stratum are the polynomials with a fixed associated graph
Quasianalytic Monogenic Solutions Of A Cohomological Equation
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Author : Stefano Marmi
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Quasianalytic Monogenic Solutions Of A Cohomological Equation written by Stefano Marmi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
We prove that the solutions of a cohomological equation of complex dimension one and in the analytic category have a monogenic dependence on the parameter. This cohomological equation is the standard linearized conjugacy equation for germs of holomorphic maps in a neighborhood of a fixed point.
Dynamics Of Topologically Generic Homeomorphisms
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Author : Ethan Akin
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Dynamics Of Topologically Generic Homeomorphisms written by Ethan Akin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The goal of this work is to describe the dynamics of generic homeomorphisms of certain compact metric spaces $X$. Here ``generic'' is used in the topological sense -- a property of homeomorphisms on $X$ is generic if the set of homeomorphisms with the property contains a residual subset (in the sense of Baire category) of the space of all homeomorphisms on $X$. The spaces $X$ we consider are those with enough local homogeneity to allow certain localized perturbations of homeomorphisms; for example, any compact manifold is such a space. We show that the dynamics of a generic homeomorphism is quite complicated, with a number of distinct dynamical behaviors coexisting (some resemble subshifts of finite type, others, which we call `generalized adding machines', appear strictly periodic when viewed to any finite precision, but are not actually periodic). Such a homeomorphism has infinitely many, intricately nested attractors and repellors, and uncountably many distinct dynamically-connected components of the chain recurrent set. We single out several types of these ``chain components'', and show that each type occurs densely (in an appropriate sense) in the chain recurrent set. We also identify one type that occurs generically in the chain recurrent set. We also show that, at least for $X$ a manifold, the chain recurrent set of a generic homeomorphism is a Cantor set, so its complement is open and dense. Somewhat surprisingly, there is a residual subset of $X$ consisting of points whose limit sets are chain components of a type other than the type of chain components that are residual in the space of all chain components. In fact, for each generic homeomorphism on $X$ there is a residual subset of points of $X$ satisfying a stability condition stronger than Lyapunov stability.
Uniformizing Dessins And Belyimaps Via Circle Packing
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Author : Philip L. Bowers
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Uniformizing Dessins And Belyimaps Via Circle Packing written by Philip L. Bowers and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Introduction Dessins d'enfants Discrete Dessins via circle packing Uniformizing Dessins A menagerie of Dessins d'enfants Computational issues Additional constructions Non-equilateral triangulations The discrete option Appendix: Implementation Bibliography.
Numerical Control Over Complex Analytic Singularities
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Author : David B. Massey
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Numerical Control Over Complex Analytic Singularities written by David B. Massey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Generalizes the Le cycles and numbers to the case of hyper surfaces inside arbitrary analytic spaces. This book defines the Le-Vogel cycles and numbers, and prove that the Le-Vogel numbers control Thom's $a_f$ condition. It describes the relationship between the Euler characteristic of the Milnor fibre and the Le-Vogel numbers.
The Conjugacy Problem And Higman Embeddings
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Author : Aleksandr I︠U︡rʹevich Olʹshanskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
The Conjugacy Problem And Higman Embeddings written by Aleksandr I︠U︡rʹevich Olʹshanskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
For every finitely generated recursively presented group $\mathcal G$ we construct a finitely presented group $\mathcal H$ containing $\mathcal G$ such that $\mathcal G$ is (Frattini) embedded into $\mathcal H$ and the group $\mathcal H$ has solvable conjugacy problem if and only if $\mathcal G$ has solvable conjugacy problem.